Debt is too a burden on our children (unless you believe in Ricardian Equivalence)

So, I was out there shovelling snow, thinking about writing a post on the burden of the debt on future generations. And about how macroeconomists' beliefs on this question had silently shifted about 30 years ago, and about how we as a profession have engaged in a sort of "memory falsification" (like Timur Kuran's concept of "preference falsification"), because we didn't want to admit that we now believe something we used to believe only unsophisticated economically illiterate rubes believed.

And I then I thought "Nah, what's the point of rehashing old ground?. Nobody nowadays believes that old "we owe it to ourselves" stuff that we used to believe."

And then I came inside and read Paul Krugman's blog post. Now I absolutely have to write the post I had decided not to write.

"That’s not to say that high debt can’t cause problems — it certainly can. But these are problems of distribution and incentives, not the burden of debt as is commonly understood. And as Dean says, talking about leaving a burden to our children is especially nonsensical; what we are leaving behind is promises that some of our children will pay money to other children, which is a very different kettle of fish."

Sorry, but that's just plain wrong. The economically illiterate rube who thinks that the national debt is a burden on our children or grandchildren is basically right. It's the exact opposite of "especially nonsensical". Unless you believe in Ricardian Equivalence.

"And you don’t have to be a right-winger to acknowledge that yes, very high marginal tax rates act as a disincentive to productive activity. So real GDP may well fall significantly.

This is what I mean when I say that the burden of debt is about incentives, not about having to deliver resources to other people.

......

The general point is that the analogy with a family that owes too much is all wrong. Unfortunately, this dumb analogy dominates our national discourse."

And I'm saying that it's not (just) about incentives, and it is about having to deliver resources to other people, and that the analogy with the family is not dumb and not all wrong (even though, like all analogies, it doesn't work perfectly).]

In the olden days we all used to believe NB. At least, all educated sophisticated people believed NB. Only uneducated unsophisticated people believed B. But we all smugly knew that "the man in the street" was wrong. In fact, a quick test for whether someone was educated and sophisticated was whether he believed B or NB. Maybe a few of us educated sophisticated people might have believed B, or didn't really understand why NB was so obviously correct, but we kept our beliefs secret, because we didn't want other people to think we were uneducated or unsophisticated rubes.

I can still remember an economics seminar at Carleton, sometime in the 1980's. The visiting speaker was an older guy, an old-school Keynesian from one of the top US universities (I have forgotten his name). Halfway through the seminar, he said "I assume that the audience here is economically literate, and that nobody here believes B?" He paused and glared around the room. The blood went to my face (a grad student told me afterwards my face was red). I raised by hand, and said that I believed B.

James Buchanan was not a sophisticated macroeconomic theorist. He didn't do macro. He did political economy/public choice. He had zero authority in macro theory. James Buchanan argued for B. But he was just a farmboy, like me. (Yes, I do have a slight chip on my shoulder; why do you ask?)

Then, all of a sudden, it seemed like all the educated sophisticated people switched to believing B. It was a very quiet revolution. There were no visible signs of argument at all. One day we all (I mean all we educated sophisticated people) believed NB; and the next day we all believed B. And we all stopped our smug condescension about the poor ignorant "person on the street" who believed B. In fact, we never mentioned the fact that we all used to believe NB. We wiped our old beliefs from our memories, like Soviet photographs. It was just too embarrassing to talk about.

There's a danger to this sort of memory wiping, and silent shifts in belief. Some people never got the memo, and still believe the old NB like we all (all educated sophisticated people) did once. Plus, it says something about our beliefs in general if we all just believe what it is fashionable to believe. (And we do, very often, which is why many of our beliefs, especially educated sophisticated beliefs, really suck).

Paul Krugman is a much better economist than me. But he never got this memo. It's time to re-open this old box of suppressed memories.

Let me make some simplifying assumptions so we can get to the heart of the distinction between B and NB. (Yes of course these assumptions are false and unrealistic, but by excluding areas where we agree we can focus on the area where we disagree.)

Suppose the government makes a transfer of 100 apples to the current cohort, financed by borrowing. Does that create a burden on future generations? Yes or no? B or NB?

I say Yes. I say B. It does create a burden on future generations. The only case where it does not create a burden on future generations is where Ricardian Equivalence holds. According to Ricardian Equivalence, the person in the street realises it will create a burden on future generations, and so saves the whole of the transfer payment, including interest, passes it on as a bequest to his children, who pass it on to their children, precisely because he wants to offset that burden on future generations.

The person on the street, in his unsophisticated uneducated ignorance, is basically right. The debt is a burden on his kids, or grandkids. Only if he anticipates that burden, and decides to offset it by increasing his bequests, a la Barro-Ricardo, does he eliminate that burden

No. My argument does not involve time travel. It doesn't require we can take apples grown 100 years from now, put them in a time-machine, send them back in time, and eat them today. But it is as if we could.

My argument is obvious. At least, it's obvious to anyone who has thought about overlapping generations models. And it's equally obvious to the unsophisticated uneducated rube who has never thought about overlapping generations models.

The government borrows 100 apples from each of cohort A, then gives each person in cohort A a transfer payment of 100 apples. It is exactly as if the government had simply given each person in cohort A an IOU for 100 apples. That IOU is a bond.

So far there is no change in cohort A's consumption of apples.

Cohort A then sells the bonds to the younger members of cohort B. So each person in cohort A gets an extra 110 apples (assume 10% interest per generation), which he eats. Cohort A then dies.

Cohort A is better off. Each member of cohort A eats an extra 110 apples. In present value terms, those extra 110 apples are worth 100 apples at the time the transfer payment is made.

Cohort B eats 110 fewer apples when young, but 121 extra apples when old, and they sell their bonds to cohort C. Although cohort B eats 11 more apples in their lifetimes, the present value of their total consumption of apples is the same. The rate of interest must be high enough to persuade them to eat fewer apples when young and more apples when old, otherwise they wouldn't have bought the bonds from cohort A. So cohort B is not worse off.

But (given my assumption) the debt is rising faster than GDP. The government knows this is unsustainable. It cannot rollover the debt forever, because eventually the next cohort will be unable to buy the bonds from the older cohort. So the government decides to pay off the debt by imposing a tax of 121 apples on each young person in cohort C, which it uses to buy back the bonds from cohort C.

Each member of cohort C eats 121 fewer apples.

Cohort A eats more apples, and cohort C eats fewer apples. It is exactly as if apples travelled back in time, out of the mouths of cohort C into the mouths of cohort A. (With interest subtracted as they travel back in time through the time machine.)

Yes, the national debt is a burden on future generations.

Can that burden on future generations be offset in some cases? Yes.

Ricardian Equivalence means that inviduals decide to offset the burden by each cohort giving rather than selling their bonds to their kids in the next cohort. So if you believe in Ricardian equivalence, you can consistently argue that the national debt is not a burden. But it's only not a burden because individuals see it is a burden and take offsetting action. That ignorant uneducated person in the street is still right.

And if the debt is used to finance investment in the kids' education then the burden is offset.

And if the interest rate is permanently less than the growth rate then the "No Ponzi" condition does not hold, and the debt can be rolled over with interest forever without taxing future generations, so cohort A eats more apples and no subsequent cohort eats fewer apples (there is never a cohort like cohort C, they are all like B).

I can relax all the other simplifying assumptions, and show that the basic message is still roughly the same. But not today.

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Observation: anemic though US growth may be, it still exceeds the nominal rate of interest on government borrowing.

That's true at this moment in time, but is it true on average? Since 1971, US nominal GDP has grown at a rate of roughly 6.8%. In contrast, the average fed rate over the period was 6.45% and the yield on US 10-year treasury bond averaged 7.15% over the same period. Depending on how you think the US government has been financing its borrowing, it isn't obvious that the no-ponzi scheme assumption is unreasonable.

More to the point, US nominal GDP per capital has only grown at a rate of 5.7% over the same period. Thus, even if the US hasn't been bound by the no-ponzi scheme condition heretofore, that's largely a function of high population growth (a ponzi scheme is sustainable if the population of suckers keeps growing). Query whether that's sustainable (it's worth noting that the no-ponzi scheme condition is biting, with extreme prejudice, in slow, or no, population growth Europe).

Plus, like others pointed out, it's like America's pay-go social security. As long as GDP keeps growing, even though Grandpa gets some of junior's stuff, junior always gets to eventually do the same when he's a grandpa.

The day GDP really stops growing very long term is the day we've really milked everything science can possibly offer. That's a day when we have robots building robots, The Matrix provides pretty much infinite resources, and don't get me started on the medical possibilities, so I don't think junior will mind.

erik: cohorts A and B are alive at the same time. Cohorts B and C are alive at the same time. Cohorts A and C are not alive at the same time. That's the simplest version.

Richard: I agree with your 2. I would say that the deficit *is* a burden, but there's an offsetting benefit too. In other words, the net benefit to the young would have been greater if the same investment in the young had been financed by taxes.

Sorry for the late reply. I'd always assumed the burden of the debt was either taxes, or too little saving and investment. If Ricardian equivilence held then just taxes. So I think I agree with you. I don't recall when things changed.

The borrowing can mean that Grandpa gets some of Junior's apples today. When Junior in the future wants his payback with interest, Grandpa is dead and he's out of luck. So Junior loses some apples. But not every junior ends up like this. Some juniors will find that Grandpa is still alive, or will have their loans go to Dad who's still alive and pays it all back with the interest.

So, some of the debt can be a loss to the young generation, but the whole thing, 100% of it a burden only to the next generation, no.

@Nick - why do you repeatedly state that bequests by bond-holders imply Ricardian equivalence? I thought we agreed that an environment where bond holders bequeath their bonds (such that there is no debt burden) could still be one in which Ricardian equivalence is violated?

In this spirit, would your title be better phrased thus: Debt is too a burden on our children (unless you believe that government bonds are transferred across generations via bequests)?

Perhaps I am being bone-headed and the consensus among economists is that any model with bequests of bonds neccessarily implies Ricardian equivalence (may be the assumptions needed for a model with bequests to violate Ricardian equivalence are totally unrealistic? - although I must say my toy model with a few wealthy dynasties and everyone else credit constrained did not sound too unrealistic as far as macro models go).

I'm thankful for your clarity and am just excited that I have understood something I find fairly complex (given my limited abilities of comprehension).

Your model posits that an apples financing/refinancing sequence puts pressure on debt math when the economy is at full employment, leading to a policy decision to replace taxes with debt. I suggested that the same full employment condition would lead to a similar MMT policy decision on taxes, for reasons of inflation pressure at full employment, but not for reasons relating to the debt math. (BTW, one of the factors whereby MMT considers debt math to be relatively benign in general is that it foresees the government being able to circumvent any prevailing “self-imposed constraint” of bond finance by issuing either reserves or very short dated debt, in which term structure risk premiums and the yield curve are no longer an issue. That gives the CB total control over the interest rate structure of government deficit financing, and allows MMT to focus much more exclusively on the issue of inflation as the rational for fiscal (or monetary) policy.)

The other thing that occurs to me is that I think MMT would see no causal linkage between a particular debt financing/refinancing sequence and reaching full employment. It’s always been interesting to me that MMT seems to eschew what I would refer generally to as “financial planning” for government deficit financing. I think this might be one of the knocks against it, although I’ve never really seen it discussed either by MMT or its critics. The default from this perspective is that MMT comes close to disregarding the entire issue of numerical representations in government financing. What I mean by that is that the size of the debt and the deficit really don’t matter at all. Neither does the mathematics of interest compounding. (Scott Fullwiller actually deals in great detail with the mathematics of interest compounding in various growth/interest rate scenarios in his detailed paper on fiscal sustainability, but the upshot of it is that there are reasons not to get too excited about it.) The variable that matters most to MMT around this issue is real capacity constraints and corresponding inflation constraints as a matter of policy. It is on this basis that MMT vociferously rejected Krugman’s earlier characterization of its views as being that “deficits don’t matter”. Deficits do matter in MMT’s view, but not for the conventional “financial planning” reasons that are related to projections of debt math. That’s all to say that I think MMT would be reluctant to wrap up the issue of full employment within a particular government deficit financing sequence even in fiat terms (and certainly not in real terms, as per apple finance). So they would question the context of your model in the sense that the full employment assumption is almost coincidental. At full employment, MTM would already be considering taxation, notwithstanding your type of debt refinancing sequence.

Wonderful discussion. Given the established conditions, what I don't understand is why government would do this:

"The government borrows 100 apples from each of cohort A, then gives each person in cohort A a transfer payment of 100 apples. It is exactly as if the government had simply given each person in cohort A an IOU for 100 apples. That IOU is a bond."

"As a matter of historical experience (using the present perfect), for the US at least (and I suspect for most large countries that borrow in their own currency and have vaguely reasonable macro policies), it generally has not been true. I assert this as per Darby, 1994 (PDF)."

This is also one of the many points in Fullwiler's paper, which he reinforces through ultimate (i.e. potential) government control over the risk free yield curve (essentially by eliminating it).

"I just got on this because JKH was talking about inheritance and seemed to be doing it the context of Nick's model (I could have missed where he introduced an alternative specification)."

Yes, some confusion there. I recognize fully that inheritance is not part of Nick's model.

I introduced it as an additional option, overlayed on Nick's model, so that inheritance and purchase both become explicit options for cohort C. If cohort C chooses not to buy bonds from cohort B, or if cohort B or any member fails to sell its bonds to cohort C, then inheritance is forced as an option. The bonds must end up with C, whether bought or inherited. If inherited, it changes the burden distribution in terms of who must be the net producer of apples, because C will end up flat consumption, even though taxed. And so on from C to B to A through regression.

“Suppose there were *one hundred* people in each cohort. Then what you say is incorrect. (That is what I was talking about when I made the distinction between what is individually rational and what is collectively rational. When there's only 1 person per cohort, collective and individual rationality of a cohort are the same thing.)”

So, I’m not seeing that.

Let’s look at the effect of the group versus the individual, first in the case of your model:

Suppose the model is set up so that each member of group C buys the same amount X of bonds from the group B.

Then suppose each member of group C is taxed for that same amount X.

So the bonds pay for the tax for each member of group C.

And having purchased the bonds with apples it might have consumed, each member of C ends up net short consumption of apples, relative to B which ended up flat consumption and A which ended up long consumption.

I think that’s your model.

Now start tinkering with an uneven distribution of bond purchases and tax liabilities across members of C. Depending on the net distribution of bonds purchased and taxes paid, the resulting distribution of the burden can be every which way, depending on the time period between bond purchase and tax payment, but ends up in the same place by the time the tax is paid.

E.g.:

If c1 purchases the same amount as his tax liability (as per your model), he ends up net short consumption as per an even distribution of shorts across the population of C as per your model.

If c2 purchases more bonds than his tax liability, he ends up the same net short consumption, but with a difference of timing in that he became extra net short consumption at the time of the bond purchase, but can now consume at the margin with his net bond redemption at the time of the bond redemption.

If c3 purchases less bonds that his tax liability, he ends up the same net short consumption, but with a difference of timing in that he became less net short consumption than otherwise at the time of the bond purchase, but now must go shorter due to the net tax liability, which brings him back to the base case of an even net short position across the full population of C.

That’s your model.

Now I’d say that if I tweak it to allow the choice of each member of C not to buy bonds at all, you’ll get a further dimension of distribution across the members of C, depending on their individual choices. I won’t go through the detail, but simply to say that any bond originally held by B that ends up not being sold to somebody in C will end up being inherited by somebody in C (as per my option adjustment to Nick's model, Adam). And you can then simply look at the resulting distribution mix across the members of C, which now includes inherited bonds as well as purchased bonds, and say that anybody who has inherited bonds has effectively pushed back the net production burden (i.e. net short consumption burden) to B or by regression to A, for that amount of bonds.

“Suppose there were *one hundred* people in each cohort. Then what you say is incorrect. (That is what I was talking about when I made the distinction between what is individually rational and what is collectively rational. When there's only 1 person per cohort, collective and individual rationality of a cohort are the same thing.)”

So, I’m not seeing that.

Let’s look at the effect of the group versus the individual, first in the case of your model:

Suppose the model is set up so that each member of group C buys the same amount X of bonds from the group B.

Then suppose each member of group C is taxed for that same amount X.

So the bonds pay for the tax for each member of group C.

And having purchased the bonds with apples it might have consumed, each member of C ends up net short consumption of apples, relative to B which ended up flat consumption and A which ended up long consumption.

I think that’s your model.

Now start tinkering with an uneven distribution of bond purchases and tax liabilities across members of C. Depending on the net distribution of bonds purchased and taxes paid, the resulting distribution of the burden can be every which way, depending on the time period between bond purchase and tax payment, but ends up in the same place by the time the tax is paid.

E.g.:

If c1 purchases the same amount as his tax liability (as per your model), he ends up net short consumption as per an even distribution of shorts across the population of C as per your model.

If c2 purchases more bonds than his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became extra net short consumption at the time of the bond purchase, but can now consume at the margin with his net bond redemption at the time of the bond redemption.

If c3 purchases less bonds that his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became less net short consumption than otherwise at the time of the bond purchase, but now must go shorter due to the net tax liability, which brings him back to the base case of an even net short position across the full population of C.

That’s your model.

Now I’d say that if I tweak it to allow the choice of each member of C not to buy bonds, you’ll get a further dimension of distribution across the members of C, depending on their individual choices. I won’t go through the detail, but simply to say that any bond originally held by B that ends up not being sold to somebody in C will end up being inherited by somebody in C (as per my option adjustment to Nick's model, Adam). And you can then simply look at the resulting distribution mix across the members of C, which now includes inherited bonds as well as purchased bonds, and say that anybody who has inherited bonds has effectively pushed back the net production burden (i.e. net short consumption burden) to B or by regression to A, for that amount of bonds.

“Suppose there were one hundred people in each cohort. Then what you say is incorrect. (That is what I was talking about when I made the distinction between what is individually rational and what is collectively rational. When there's only 1 person per cohort, collective and individual rationality of a cohort are the same thing.)”

So, I’m not seeing that.

Let’s look at the effect of the group versus the individual, first in the case of your model:

Suppose the model is set up so that each member of group C buys the same amount X of bonds from the group B.

Then suppose each member of group C is taxed for that same amount X.

So the bonds pay for the tax for each member of group C.

And having purchased the bonds with apples it might have consumed, each member of C ends up net short consumption of apples, relative to B which ended up flat consumption and A which ended up long consumption.

I think that’s your model.

Now start tinkering with an uneven distribution of bond purchases and tax liabilities across members of C. Depending on the net distribution of bonds purchased and taxes paid, the resulting distribution of the burden can be every which way, depending on the time period between bond purchase and tax payment, but ends up in the same place by the time the tax is paid.

E.g.:

If c1 purchases the same amount as his tax liability (as per your model), he ends up net short consumption as per an even distribution of shorts across the population of C as per your model.

If c2 purchases more bonds than his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became extra net short consumption at the time of the bond purchase, but can now consume at the margin with his net bond redemption at the time of the bond redemption.

If c3 purchases less bonds that his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became less net short consumption than otherwise at the time of the bond purchase, but now must go shorter due to the net tax liability, which brings him back to the base case of an even net short position across the full population of C.

That’s your model.

Now I’d say that if I tweak it to allow the choice of each member of C not to buy bonds, you’ll get a further dimension of distribution across the members of C, depending on their individual choices. I won’t go through the detail, but simply to say that any bond originally held by B that ends up not being sold to somebody in C will end up being inherited by somebody in C (as per my option adjustment to Nick's model, Adam). And you can then simply look at the resulting distribution mix across the members of C, which now includes inherited bonds as well as purchased bonds, and say that anybody who has inherited bonds has effectively pushed back the net production burden (i.e. net short consumption burden) to B or by regression to A, for that amount of bonds.

“Suppose there were one hundred people in each cohort. Then what you say is incorrect. (That is what I was talking about when I made the distinction between what is individually rational and what is collectively rational. When there's only 1 person per cohort, collective and individual rationality of a cohort are the same thing.)”

So, I’m not seeing that.

Let’s look at the effect of the group versus the individual, first in the case of your model:

Suppose the model is set up so that each member of group C buys the same amount X of bonds from the group B.

Then suppose each member of group C is taxed for that same amount X.

So the bonds pay for the tax for each member of group C.

And having purchased the bonds with apples it might have consumed, each member of C ends up net short consumption of apples, relative to B which ended up flat consumption and A which ended up long consumption.

I think that’s your model.

Now start tinkering with an uneven distribution of bond purchases and tax liabilities across members of C. Depending on the net distribution of bonds purchased and taxes paid, the resulting distribution of the burden can be every which way, depending on the time period between bond purchase and tax payment, but ends up in the same place by the time the tax is paid.

E.g.:

If c1 purchases the same amount as his tax liability (as per your model), he ends up net short consumption as per an even distribution of shorts across the population of C as per your model.

If c2 purchases more bonds than his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became extra net short consumption at the time of the bond purchase, but can now consume at the margin with his net bond redemption at the time of the bond redemption.

If c3 purchases less bonds that his tax liability, he ends up with the same net short consumption position, but with a difference of timing in that he became less net short consumption than otherwise at the time of the bond purchase, but now must go shorter due to the net tax liability, which brings him back to the base case of an even net short position across the full population of C.

That’s your model.

Now I’d say that if I tweak it to allow the choice of each member of C not to buy bonds, you’ll get a further dimension of distribution across the members of C, depending on their individual choices. I won’t go through the detail, but simply to say that any bond originally held by B that ends up not being sold to somebody in C will end up being inherited by somebody in C (as per my option adjustment to Nick's model, Adam). And you can then simply look at the resulting distribution mix across the members of C, which now includes inherited bonds as well as purchased bonds, and say that anybody who has inherited bonds has effectively pushed back the net production burden (i.e. net short consumption burden) to B or by regression to A, for that amount of bonds.

Nick: Nice post and very nice discussion too. However I still think that Paul is basically right. Everything depends on how you define what "our children" means in your overlapping generations model. If you take it literally, that it means next generation directly, then you are right.

But there is other possible way of looking at these things. Let's consider that at every moment there are just two generations - adults and children. Adults produce things, children by definition do not produce. Suddenly the borrowed consumption of the first generation is just redistribution within the generation. Some portion of this generation that bought bonds happen not to consume and other that have bonds actually did consume more - however, the total level of consumption of that generation is the same and that is 1000 apples. Let's move 200 years ahead when some future generation decides not to roll-over the debt. But it is still a wash. Apple production is still the same 1000 apples as it was 200 years ago, that means that some portion of that last productive generation was tricked to consume less, but then other part of that generation just consumed more. However that last productive generation as a whole still consumed 1000 apples it produced. If you consider this 200 year distant people as your grand-grand-grand children, then they as a whole were not at all affected by your debt. Some of them that were holding the bonds were - but then other happened to consume more exactly as to offset this "injustice". The debt had no effect on real production of apples - all it did was just redistribution within that generations with potential incentive effects.

I think I follow you here. And I think I basically agree. This is very hard to explain clearly, and put the MMT and my perspectives into a common framework, but let me try this:

Assume for simplicity that the national debt is one big savings account that pays interest and can be cashed out and spent at any time. The government can adjust the interest rate daily.

Suppose we are currently exactly at full employment, but the national debt is growing over time as interest accumulates, and nothing else is changing over time. When next year rolls around, and the debt is larger, people will be unwilling to hold the extra debt. They want to cash part of it out, and spend it. The government has 3 choices:

Update: Maybe I should think more before posting. The thing I did was just getting rid of overlapping generations condition. But I still think that the redistributive argument is basically right. If the whole unraveling of the ponzi scheme would happen within the first generation, then it would be just redistribution within that generation. The point is, that issuing debt IS redistribution within that original generation. Income of that generation as a whole - if you measure it as the sum of all things produced and sold within economy - remained the same at 1000 apples. In Nick's model this income was never lowered.

I also get that line of argument about game theory, when buying bonds is the rational thing to do - if you expect that interest will be paid. And that you may pass the risk of not paying interest down to next generation. But that is still just a way of redistribution. It is just very innovative in a way that it is very appealing to everybody that is part of this scheme - and this would be a valid argument against too much debt. But the point is that the argument would be based on unjust redistribution of wealth for our distant grandchidlren, it would not be based on the premise that our grandchildren would be poorer in terms of not being able to produce less.

So it everything goes down to the question. What is income and what does it mean to be rich or to be poor, and especially what does it mean for a whole generation? Are you rich if you get to consume more, or alternatively are you rich if you get to produce more? I think Paul thinks of national accounting and he is right that if you define income of a generation by looking at GDP they produce, than it remains at stable 1000 apples. But if you look at it as number of apples they get to consume they may be poorer.

According to the general thrust of the model, at some point, the government taxes to redeem bonds.

Whoever ends up holding those bonds at maturity has forgone consumption by not selling them to somebody else within a time period of epsilon to maturity, and consuming with the proceeds instead.

Nick’s model defines that group as cohort C, by construction.

Cohort C is therefore net short consumption, compared to some (imaginary) alternative world, in which C might have sold their bonds to cohort D, and consumed with the proceeds. However, in that imaginary alternative world, it is also important that the tax liability be passed from C to D. Otherwise, while C would end up flat instead of net short consumption, it would now end up net short a tax liability and be equally poor as in the model case.

So it is important for example that when B sells the bonds to C, B also gets rid of its potential tax liability. I’m not sure that’s perfectly clear by the construction of the model, although it’s implied I think.

So with that, those who hold the bonds at maturity that are redeemed with taxes at maturity, are left holding the bag in terms of forgone consumption, and have a net short position in consumption relative to the flat or long positions of their predecessors.

henryc: "In what way would it interest government to take this action?"

Fair question.

1. Because cohort A is larger than the normal cohort and/or more self-indulgent than the normal cohort and/or less constrained by "old-fashioned prejudices" about debt (i.e. it has read Abba Lerner) and votes in a government that's good for cohort A. (James Buchanan "Democracy in Deficit" is good on this subject, IIRC.)

2. Because there unemployment and cohort A wants fiscal policy to fix it.

3. Raise the interest rate higher to persuade people to keep holding the larger debt."

The key is the full employment assumption. That would very likely translate to inflation risk in the MMT view. And that would translate to an MMT prescription for marginal policy tightening. MMT prefers fiscal tightening, but can work within the existing framework of either fiscal or monetary tightening or both. Since we’re looking at tax contingencies here, let’s stick with the fiscal tightening option.

So MMT would consider higher taxes as one of the fiscal tightening options.

This is separable from the issue of assessing the flow of funds as you’re looking at it. MMT would simply not accept the premise that “people are unwilling” to hold the debt at current levels as a result of debt accumulation and full employment and inflation pressures. MMT rebukes the notion of insolvency for a fiat issuer (assuming we’re talking about fiat here; as I said, I don’t think MMT would shed any light on an apples finance economy).

So the idea that “people are unwilling” would not enter into it from an MMT perspective. Given the operational options that the government and the central bank have for anything right up to and including captured reserve issuance, solvency and willingness to hold the instrument of deficit financing simply is not an issue.

The issue is real capacity and inflation risk, not financing appearances.

So MMT would tighten fiscal policy with taxes, in this example. And that would allow retirement of debt, at least at the margin. That would steer MMT toward # 2 in recognition of the real capacity and inflation constraints.

Your point about “letting them cash out” is a little problematic from an MMT perspective. The public doesn’t normally “cash out” debt with the government at the macro level. That would simply involve a conversion of maturing debt to banks reserves (and corresponding deposit liabilities), instead of rolling over the debt. MMT is pretty much neutral on the relevance of the reserve/currency/bond mix, in general. Moreover, the public doesn’t need more bank reserves and deposits from this source to achieve its spending desires. It can easily ramp up its money stock and velocity through commercial bank borrowing (“horizontal” finance in the terms of MMT), in the momentum of an inflationary froth. In fact, Fullwiler considers it a particularly relevant operational point that government bonds are easily used as collateral for bank borrowing.

3. Raise the interest rate higher to persuade people to keep holding the larger debt.

The key is the full employment assumption. That would very likely translate to inflation risk in the MMT view. And that would translate to an MMT prescription for marginal policy tightening. MMT prefers fiscal tightening, but can work within the existing framework of either fiscal or monetary tightening or both. Since we’re looking at tax contingencies here, let’s stick with the fiscal tightening option.

So MMT would consider higher taxes as one of the fiscal tightening options.

This is separable from the issue of assessing the flow of funds as you’re looking at it. MMT would simply not accept the premise that “people are unwilling” to hold the debt at current levels as a result of debt accumulation and full employment and inflation pressures. MMT rebukes the notion of insolvency for a fiat currency issuer (assuming we’re talking about fiat here; as I said, I don’t think MMT would shed any light on an apples finance economy).

So the idea that “people are unwilling” would not enter into it from an MMT perspective. Given the operational options that the government and the central bank have for anything right up to and including captured reserve issuance, solvency and willingness to hold the instrument of deficit financing simply is not an issue.

The issue is real capacity and inflation risk, not financing appearances.

So MMT would tighten fiscal policy with taxes, in this example. And that would allow retirement of debt, at least at the margin. That would steer MMT toward # 2 in recognition of the real capacity and inflation constraints.

Your point about “letting them cash out” is a little problematic from an MMT perspective. The public doesn’t normally “cash out” debt with the government at the macro level. That would simply involve a conversion of maturing debt to banks reserves (and corresponding deposit liabilities), instead of rolling over the debt. MMT is pretty much neutral on the relevance of the reserve/currency/bond mix, in general. Moreover, the public doesn’t need more bank reserves and deposits from this source to achieve its spending desires. It can easily ramp up its money stock and velocity through commercial bank borrowing (“horizontal” finance in the terms of MMT), in the momentum of an inflationary froth. In fact, Fullwiler considers it a particularly relevant operational point that government bonds are easily used as collateral for bank borrowing.

primed: "In this spirit, would your title be better phrased thus: Debt is too a burden on our children (unless you believe that government bonds are transferred across generations via bequests)?"

1. Because "Ricardian Equivalence" is shorter.
2. Because I'm being sloppy.
3. Because the set of economists who believe in bequests that offset 100% of the burden on future generations and who do not believe in Ricardian Equivalence is probably an empty set.
4. Because I'm a bad boy and want to tease the Keynesians who believe in No Burden and who don't believe in Ricardian equivalence. ;-)

JV: It's the cohort(s) that get the transfers that get the benefit. It's the cohort(s) that get taxed that bear the cost. The two sets might not overlap at all, if the first group are all dead before taxes get increased. It could be our great great gandkids who bear the burden.

"At one extreme, if the government rolls over the debt and waits 70 years or more before increasing taxes, 100% of the burden will be borne by future generations."

But then it doesn't happen because, in fact, the game is essentially infinite and GDP always keeps growing very long term (about as much as debt). (The day GDP really stops growing very long term is the day we've really milked everything science can possibly offer. That's a day when we have robots building robots, The Matrix provides pretty much infinite resources, and don't get me started on the medical possibilities, so I don't think junior will mind.)

Yes, the debt means that some grandpas will get some juniors' apples in the future. And/or some grandpas will get will get some juniors' apples in the present, and never pay it back in the future.

But, that generation of juniors will be able to do the same thing in the future when they're grandpas (with interest, that will be payable due to ever expanding GDP very long term).

A big problem is this, "But (given my assumption) the debt is rising faster than GDP." You're assuming that this will continue to happen in the US until at some point we default, and young debt holders never get paid. I think we will wise up before it comes to that and stop voting for Republicanism so much in its devastating, anti-thinking, modern form. So very long run we will keep our debt to a tenable level of GDP, or maybe even pay it all off in the not too far future, if we can stop voting for the toxic Republican Party so much.

With the details of the way I think the world and the United States actually works, and will work, it's far far closer to Krugman's description, than the popular description of our children taking a total loss on 100% of the debt we take out today. And Krugman was just trying to give a big reason/intuition why the popular description of a 100% loss to our children is false.

"In what universe does PK have an obligation to respond to every notoriety-seeker who critiques him?"

'He doesn't, but it would be really good if he did in this case. And not just good for me, but good because this is an important policy question, and he's very influential.'

-I read his silence as saying he either assents that you have a good point and there's nothing to argue about (or time to do it), or that he needs more time to work his thoughts out. Either way, a point or two in your column.

"You've said your piece; you can safely assume he's read it."

'I honestly don't know if that's a safe assumption or not. My assumption is that he probably hasn't. It would be good if I'm wrong.'

-True. Though given the viciousness you've thrown at him, and the fact that he does check in here from time to time, I'd put odds at 5:1 he's at least aware.

"Now move on."

'Back to grading exams? Easier said than done!'

Ain't that the truth. ! Though if you Canadians still get to be working on it, lucky you! We had to get grades done 3 weeks ago!

Paul: "-I read his silence as saying he either assents that you have a good point and there's nothing to argue about (or time to do it), or that he needs more time to work his thoughts out."

I really hope it's the "...needs more time to work his thoughts out." bit. It took me a helluva long time to work my own thought out on this, and even though he's gonna be quicker than me, that could still be time.

This whole question is like one of those duck/rabbit drawings. Both visions are appealing. It's hard to see them both at the same time.

"Though given the viciousness you've thrown at him,..."

I honestly don't think I was being vicious. It's always a bit nervous-making though, when you know you are taking on someone bigger and stronger and better than you. I did need to come out hard, and say he was wrong, but I thought I was being respectful. (And that respect is very genuine, even if I do think he's wrong in this case.)

It seems to me that a net intergenerational transfer of resources (be they apples or output more generally), must always, as a point of logic, be regarded as a burden for somebody, since--as any MMTer should agree--someone's surplus is always someone else's deficit.

If the govt can simply expand and contract the supply of apples as some function of the unemployment rate (or whatever), then this does affect matters. If the economy grows at a faster rate than the value of the debt, then this does likewise. But in either case, there is still the initial burden which must be compensated for by greater supply. (Having to "roll over" the burden forever should also be regarded as a cost).

And isn't there an issue regarding the composition of output? Say that the next generation isn't so interested in apples. Well, now the economy is geared up to overproduce them. That's a real cost that must be borne as well.

Nick, JKH, Peden, et al, I will get back to this, no time now, but thanks JKH for all the leg work. In the meantime, Nick, there is STILL nothing 'unsustainable' about issuing the debt. There is just inflation, maybe eventually really bad inflation.

Yep. And that really is the underlying point here. It's just that we have to switch our minds from the standard way of doing the accounts to a sort of intergenerational accounting, in order to see this point.

Nice post and discussion. But I hope you'll do a post sometime soon addressing whether or not too much private debt is or can be a problem. (Spain?) Most people seem to think it is, but they rarely say why. My own thought is that financing via debt rather than equity reduces your flexibility in responding to changed circumstances, and changing circumstances is what creative destruction is all about. But I don't know how I'd model this.

On the other hand, the constraints imposed by debt contracts reduce the scope of principal-agent problems, so the optimal amount of private debt is not zero.

3. Raise the interest rate higher to persuade people to keep holding the larger debt."

The key is the full employment assumption. That would very likely translate to inflation risk in the MMT view. And that would translate to an MMT prescription for marginal policy tightening. MMT prefers fiscal tightening, but can work within the existing framework of either fiscal or monetary tightening or both. Since we’re looking at tax contingencies here, let’s stick with the fiscal tightening option.

So MMT would consider higher taxes as one of the fiscal tightening options.

This is separable from the issue of assessing the flow of funds as you’re looking at it. MMT would simply not accept the premise that “people are unwilling” to hold the debt at current levels as a result of debt accumulation, full employment and inflation pressures. MMT rebukes the notion of insolvency for a fiat issuer (assuming we’re talking about fiat here; as I said, I don’t think MMT would shed any light on an apples finance economy).

So the idea that “people are unwilling” would not enter into it from an MMT perspective. Given the operational options that the government and the central bank have for anything right up to and including captured (i.e. forced) reserve issuance, solvency and willingness to hold the financial instrument of deficit financing simply is not an issue.

The issue is real capacity and inflation risk, not financing appearances.

So MMT would tighten fiscal policy with taxes, in this example. And that would allow retirement of debt, at least at the margin. That would steer MMT toward # 2 in recognition of the real capacity and inflation constraints.

Your point about “letting them cash out” is a little problematic from an MMT perspective. The public doesn’t normally “cash out” debt with the government at the macro level. That would simply involve a conversion of maturing debt to banks reserves (and corresponding deposit liabilities), instead of rolling over the debt. MMT is pretty much neutral on the relevance of the reserve/currency/bond mix, in general. Moreover, the public doesn’t need more bank reserves and deposits from this source to achieve its spending desires. It can easily ramp up its money stock and velocity through commercial bank borrowing (“horizontal” finance in the terms of MMT), in the momentum of an inflationary froth. In fact, Fullwiler considers it a particularly relevant operational point that government bonds are easily used as collateral for bank borrowing.

The whole "crowding out" thing, of course, is not so obvious. Risky investments crowd out other risky investments; this is obvious from any basic asset pricing framework (e.g. CAPM). But default free T-Bills of an inflation targeting government aren't risky. If they "crowd out" (excess demand for savings), then rates can be lowered. And if there's an asset bubble, rates can be raised. If rates are set effectively the stock of T-Bills just sits there compounding away, no cash flows ever exchanged with the real economy, taxes never affected. How can they affect anything? In Ball and Mankiw the crowding out is a back-of-the-envelope assumption. There simply is no way to get it as a theoretical *result*. The way I see it, depending on the short rate, a large quantity of outstanding T-Bills is equally likely to cause "crowding in" (inflation) as crowding out (deflation). I think there might be a case, that the greater the ratio of T-Bills to real assets, the greater the sensitivity of the system to a slight misspecification of the short rate and the greater the likelihood that we will suddenly spiral away into deflation or inflation. But I don't see an inherent bias in either direction (apart from the ZLB).

JHK, Nick - I published the duplicate posts that were accidentally deleted by the spam filter. I hope it doesn't make things too confusing; I understand that the thing to do is 'train' the algorithm so that it might recognise what sort of posts are rescued.

The Problem:
There is a steady state economy with a constant population in which each generation produces 1000 apples. For some reason Generation A consumed 1110 apples, convincing Generation B to give it 110 apples. It did so via gov't bonds which it bought for 100 apples, which paid out 110 apples at maturity. (The gov't returned the 100 apples to Generation A after the sale. God knows why. ;)) When the bonds matured, the gov't sold 110 apples worth of bonds to Generation B to pay Generation A. The bonds it sold to Generation B also pay out 110 apples per 100, so Generation B stands to collect 121 apples at maturity.

The problem is that, thanks to the magic of compounding, if Generation C buys 121 apples worth of bonds to pay back Generation B, and then Generation D buys 133.1 apples worth of bonds to pay back Generation C, etc. some generation will eventually be unable to buy all of the gov't bonds. A more serious problem is that each succeeding generation consumes a greater proportion of the output of apples, effectively impoverishing its children. The society would like to return to a steady state, without penalizing any generation after Generation A. How is that possible?

Solution 1:

When Generation B's bonds mature, the gov't sells 121 apples worth of bonds to Generation C. Then it taxes Generation B to the tune of 11 apples, which it uses to by 11 apples worth of bonds from Generation C, leaving it with 110 apples worth of bonds. Also, the bonds that it sells to Generation C are 0% bonds, which it calls "money". ;) When those bonds mature, Generation C can cash them in for 110 apples, which the gov't buys from Generation D with new money. (As it turns out, many people in Generation C have already used their money to buy apples from people in Generation D before the money matures, so that many people in Generation D are happy to exchange their old money for new money instead of selling apples.)

Solution 2:

As in solution 1, the gov't extracts 11 apples from Generation B via taxes after their bonds mature. However, the economy already has money. So the bonds that the gov't sells to Generation C are denominated in money, not apples. And when they mature, lo and behold, inflation has made them worth only 110 apples, exactly what they were worth originally. OC, the gov't has tinkered with inflation to make that happen. ;) Gov't tinkering is not perfect, but things are close enough to a steady state that people are content.

There are other solutions, of course. :) My favorites are those where there is a big celebration every year where everybody dances on the graves of Generation A and the younger generation gives some apples to the older generation. Solution 2 looks something like the modern world, with inflation and nominally increasing gov't debt.

"No I'm not. I'm assuming that *either* there's a default *or* taxes get raised (*or* expenditures get cut). In either case, there's a burden of whoever is alive when that eventually happens."

You are correct, except that's IF it happens, not eventual when. The economy can grow faster than the debt, making the current tax rate (or even a smaller one) eventually big enough to retire the debt.

So this is a young versus old thing, but it's a complicated one, more complicated than your post makes it look. If we're deficit spending so that we can give more money to seniors in Social Security, then yes, we may be transferring money from young to old (but this is largely true with tax paid money too, as seniors pay little taxes). But maybe not, if GDP grows faster than debt, the young will get their chance eventually and will be no worse off. And if the borrowed money is not being transferred to seniors, but spent on high return investments that benefit the young, then certainly as a group the young are better off as a result.

But yeah, it's theoretically possible some young may be left in the lurch. I'd like to see a cite for a paper that goes through this with everything vetted mathematically. But, let me try a very simple model.

Two person country: 20 year old Junior and 70 year old Grandpa. Junior loans the government $100K. The government gives the $100K to Grandpa as an old age pension.

30 years later, when Grandpa's gone, Junior gets taxed $100K plus interest to pay off the government bond he holds; out one pocket, in the other. Then, the government says we're done deficit financing pensions; we want to pay as we go now; so give us the present value of your $100K in future pension.

Grandpa got a free pension, and Junior paid for two, but only got one.

I know Nick was making a somewhat contrived example to make the point simply and clearly but in general there can be very good reasons for the government to bring these bonds into existence and it wouldn't be the case that society would like to return to a steady state, without penalizing any generation after Generation A.

One reason that these bonds may be serving a social purpose is if people are more productive when young than when old, remember that each generation lives for two periods. What if they produce 1000 apples when young but only 500 when old? They then might prefer to arrange with other cohorts so everyone can eat 750 apples in each period of their life.

This is possible but requires an arrangement where each young cohort gives the current old cohort 250 apples on the understanding that they'll get the same favour from the next, not yet born, young cohort.

Issuing bonds backed by the power to tax is how the government promises the current young cohort that they'll be able to collect their apples when old, thus making them willing to give up some apples when young in excahnge for the bonds.

The country consists of one million 20 year old Juniors and one million 70 year old Grandpas. The Junior loans the government $200K each. The government gives the $200K's to the Grandpas as an old age pension.

30 years later, when the Grandpa's are gone, the Juniors gets taxed $200K each plus interest to pay off the government bonds they hold; out one pocket, in the other. Then, the government says we're done deficit financing pensions; we want to pay as we go now; so all Juniors give us the present value of your $200K in future pensions.

The Grandpas got a free pension, and the Juniors paid for two, but only got one.

Just to add to Adam P.'s 3.51 comment: his example would be exactly the sort of case where you would expect to see the real interest rate less than the growth rate. Before the government sets up the pension plan, the real interest rate could well be negative, because the young would want to pay to lend apples to eat when they are old and have fewer apples.

"And I then I thought "Nah, what's the point of rehashing old ground?. Nobody nowadays believes that old "we owe it to ourselves" stuff that we used to believe.""

Its not likely Krugman believes what he is writing. You need some current events context here. Obama is trying to pivot the national conversation away from sovereign debt back to jobs. Krugman's position at the NYTs is primarily to sell the administration's story of the week. See for instance his blithe indifference to his own academic publications on liquidity traps. This recent jobs pivot became important because we just had a debate on the payroll tax cut.

Obama took the position that the payroll tax cut was essential to the jobs agenda. The opposition took the position that further fiscal stimulus (we're running a deficit at 10% of GDP right now) wasn't appropriate at this stage of the recovery.

Now that the debate is over, Krugman is trying to make sure the opposition didn't just have a 'policy difference'; he wants people to think they are ignorant. Since this is a political issue, don't expect the profession to come down on him hard. The ends justify the means.

I'm having trouble with the idea that useful conclusions can be reached with the assumptions given.

Money borrowed from the "future" can very well be "invested" -- though whether nor not it will is a very different question.

Technology and productivity improvements are very able to change the nature of output. We do not even have to assume that technology is developed with our own local resources.

Future generations can default on the debt that has been left for them to pay off. In this way they may incur obligations or consequences of less cost than paying off the debt.

Wars, or other changes to political entities, can vastly change the relevance of prior activities or obligations.

Now, all that said, I am not suggesting that large debts are good or that we should be leaving such debts for future generations! However, to use the family debt analogy in the opposite mode, there are times when it is appropriate for a family to incur debt and pay it back over time. Are there such occasions for a nation state?

Daniel: think it through. When people say it is *impossible* for debt to create a burden on future generations (except through lower capital stock, borrowing from abroad, disincentive effects from taxation, etc.) then all I need is *one* counter-example to show that what they are saying is wrong.

Which I have provided.

And the underlying insight of this simplified model can survive the introduction of money, and growth. Read some of the comments above.

If I had used a simple model that confirmed, rather than contradicted, your previous views, would you have objected to its simplicity?

OK, I am happy to concede that point and go along with you in criticizing the "impossible" verbiage. You have definitely achieved that one.

I'm still not quite sure why I should buy into the "debt places a burden on our children" talk or the "we need to tighten our belts just like responsible families" talk. It seems to have much more fundamentally wrong with it than Krugman's view.

And the thing is, you seem to admit this yourself at the end of your post.

(And in my view, the "uneducated rube" thing has nothing to do with it - there have been other times when public investments and bond sales were embraced by the "uneducated rube").

As for this: "If I had used a simple model that confirmed, rather than contradicted, your previous views, would you have objected to its simplicity?", I think you're missing my point. Simplicity is not the problem at all. Simplicity is a virtue in modeling.

Let's set the "impossible" question aside, because I don't think any of Krugman's posts were really trying to take a stand on that particular word.

Let's say the question is: "Is public debt like personal debt - if we contract public debt does that mean that the public's future is burdened in the same way that when we contract personal debt our future is burdened by repayment?"

The answer to that question seems to me to be "no - it's quite different from personal debt", and it seems to me that we need to try to prevent that sort of sneaking of microeconomic thinking into macroeconomics.

Daniel: "I'm still not quite sure why I should buy into the "debt places a burden on our children" talk or the "we need to tighten our belts just like responsible families" talk."

I believe that "debt places a burden on our children" (assuming the No-Ponzi Condition is satisfied), but it doesn't necessarily follow that "we need to tighten our belts".

Almost any policy has benefits as well as costs. In some cases, the benefits of running a deficit (to us, and/or to our children) exceed the costs to our children, and we should run a deficit in those cases. Just because a policy has costs doesn't mean we shouldn't do it. But we do need to be clear about those costs, and not pretend they don't exist.

"(And in my view, the "uneducated rube" thing has nothing to do with it - there have been other times when public investments and bond sales were embraced by the "uneducated rube")."

That's more of an aside to the main argument. It's just that I am embarrassed, as an economist, that we economists spent decades (between WW2 and around 1980) smugly thinking uneducated rubes were wrong about the debt being a burden on future generations. And then we (mostly, after around 1980) very quietly changed our minds and decided the uneducated rubes were right after all.

When I borrow money, it's my name on the IOU. I get the benefit, and I pay the cost.

When the government borrows money and gives it to me, the name on the IOU is left blank. It will be filled in at some future date by some future government putting the name of some future taxpayers on that IOU. It might be me, in 10 years time. It might be my kids, or grandkids...but it isn't necessarily going to be me and my generation. Now, if you think in dynastic terms, and assume I will make an appropriate offset in my will for my kids and grandkids,...then it's different. But in that scenario you are starting to open up the whole Ricardian equivalence kettle of fish. And do you really want to go there, if you are trying to explain why you need a deficit now?

While we can grow our way out of our debt problems it doesn't change the basic analysis that debt burdens future generations. Even if the wealth of future cohort is growing even given the reduction in debt, their wealth would have been that much greater if they did not have to service the debt of previous generations. When we say there is a burden it does not necessarily have to mean that the burden is going to completely destroy all economic opportunities of the generation that pays even though cases like that are the most visible, ie Greece.

Bringing in the dynamics of growth or recession just adds an unnecessary factor.

Adam P: "in general there can be very good reasons for the government to bring these bonds into existence and it wouldn't be the case that society would like to return to a steady state, without penalizing any generation after Generation A."

The welfare of future generations is a precondition of the debate. Otherwise it's, "Is the debt a burden on future generations? Who cares?"

Nick's assumed gov't policy guarantees that it will be a burden on someone in the future. But it is possible to assume a steady-state gov't policy. :)

I agree that Paul Krugman is wrong. To rephrase the essence of your argument in an even simpler way: Suppose the government borrows $10,000 from me, and burns the money. This creates a $10,000 debt burden, even though "we owe it to ourselves." If the government increases Joe's taxes by $10,000 (ignoring interest) to pay me back, Joe is $10,000 poorer and I have the same amount of money I had before. If the government borrows from somebody else to pay me back, that just kicks the debt can down the road.

But I am suspicious of the intergenerational part of your argument. Could it not be generalized to reach the absurd conclusion that any expenditure of money or of apples is ultimately wasted, because everyone who might benefit from the expenditure will eventually die?

I have another point to make, sorry if it was already said in some of the post before me. The issue is that Nick stops the game with the last generation being taxed and paying for the debt. But what if I would say that the game end just one generation later? And that generation would be able to capitalize on their fathers effort to pay down old debts and they could build their own debt bubble (since the debt is now lower or zero). So it may very much be so that in total the consumption of those future generation remains.

This is the point. If you count with infinite number of future generations, then it does not make sense to speak about real burden of debt. Or to get too philosophical here, you may say that by using the debt bubble now we deprive our children to do such con themselves. But since we know that these tricks will happen again over and over throughout the history it really should not matter at all.

Jim: "What happens when the debt roll over is say, 20-30% of world GDP? Who is going to roll all that over?"

It already is well over 20-30% of GDP in most countries around the world.

Alan T. "But I am suspicious of the intergenerational part of your argument. Could it not be generalized to reach the absurd conclusion that any expenditure of money or of apples is ultimately wasted, because everyone who might benefit from the expenditure will eventually die?"

I didn't say it was wasted. Cohort A enjoyed it. Cohort C paid for it. There's a benefit, and a cost. But the cost and benefit don't happen to the same people.

JV: Well, we could talk about the burden of the existing debt, relative to no existing debt. Or we could talk about how good we are to future generations by not expanding the debt up to its maximum. Sure, there always has to be some sort of baseline, against which we can talk about costs and benefits.

"Well, we could talk about the burden of the existing debt, relative to no existing debt. Or we could talk about how good we are to future generations by not expanding the debt up to its maximum. Sure, there always has to be some sort of baseline, against which we can talk about costs and benefits."

we should also include the benefits of having risk-free and liquid financial assets such as tsy's available

studentee: "we should also include the benefits of having risk-free and liquid financial assets such as tsy's available"

Yep. That's a question I ought to understand better, and try to understand better, but keep failing to understand better. I have started a couple of blog posts on that subject, and abandoned them, because my thoughts are just too muddled to be worth posting.

Min: "The welfare of future generations is a precondition of the debate"

Yes, that's my point! The introduction of the bonds can be welfare improving, thus we are NOT trying to return to the bondless status quo.

Further, the welfare improvement could easily be large enough that if a transitory shock hits that makes a previously sustainable arrangement not work for a particular generation the government who is interested in the welfare of future generations may find that it perfers to penalize the current generation with taxes instead of defaulting because if it defaults it won't be able to continue the arrangement with future generations.

Victim C will be dodging potholes to keep his old car from getting beat into scrap metal and will wondering why he pays so much in taxes and his child is using a 20 year old text book. It'll be because his government is using half of its revenue to pay bond holders he doesn't see. So he'll cheat on his taxes so that he can buy that new car instead, but one day an IRS agent shows up at his door with a gun on his hip and says, "good day, Victim C. Please hand over x amount or we will sell your home or throw you in jail. But remember, it's no burden, it's merely a dead politician's promise that you would be forced to give money to bond holder a."
I don't understand Krugman. I know he's not an idiot so I must assume that he's disengenious. That his political philosophy interferes with his reason. There is only one essential question: Will my sons be worse off (even if their tax burden is identical to mine) than me when debt payments as a percentage of revenue increase?

Grant: remember, 30 years ago nearly all(?) of us macroeconomists thought the same way, that the debt is not a burden, because we owe it to ourselves. When you have read Abba Lerner on Functional Finance, it feels very convincing. After all, apples can't travel back in time, can they!

Cohort B has no incentive to buy Cohort A's IOU unless Cohort B is totally incapable of pricing debt. Is that one of the assumptions? Doesn't Cohort B know there is no growth in the economy? Why would they expect a 10 percent rate of interest? They just wouldn't pay that and Cohort A would eat the IOU's or accept a discounted price.

Nick’s burden thesis is certainly correct, GIVEN THE ASSUMPTION that generation A sells bonds to generation B. And B sells to C, etc etc. And this certainly happens to some extent in the real world in that oldies sell bonds in their retirement, and youngsters building up their savings buy said bonds.

But the $64k question is whether, given an INCREASE in government debt, people increase their pension pot to any significant extent. And my answer to that is a resounding “no”.

In fact if there were no government debt at all, people would make much the same pension provision as where government debt exists: they’d just use different assets and/or go for pay as you go or “unfunded” pension schemes. (And the latter incidentally involves youngsters supporting oldies, just as much as where youngsters buy bonds from oldies.)

Ergo, the creation of government debt, or an increase therein has a negligible effect on the burden imposed on future generations (or the benefit passed on to future generations if all govt debt funds investments like infrastructure). At least that’s true assuming no big change in debt bought by foreigners, which is slightly unrealistic assumption.

* govt debt is owed in a real variable the government doesn't produce (apples). With zero growth and positive interest it is only a matter of time when the price of bonds will be more than what some generation will be able to produce so the intergenerational transfer will not be able to happen.

In reality though (and this is what PK discussed) the govt intergenerational debt is a promise to exchange one govt IOU for... another, of which the govt can produce costlessly an unlimited amount.

I am definitely an economic layman, but it seems to me this model is simplified one level too far to be comparable to what Krugman is talking about. Krugman's point seems to be that on the aggregate debt is not a burden to future generations, but is not speaking to individual situations. To be relevant I would think there needs to be one more set of cohorts. so let's call it Cohort AW (A wealthy) and Cohort AP (A Poor), both halves of he same economy. The government wants to run a deficit (for good or bad) so it borrows apples from where apples exist, the backyards of Cohort AW. It then lends the apples to Cohort AP and gives IOU/Bonds to Cohort AW. Assume 10% apple interest over the generation. Assuming Cohort AP can only pay back the 10%, in the first generation Cohort AW will have consumed 90 less apples (100 lent and 10 received back) and AP will have consumed 90 more apples (100 borrowed and 10 paid back). We have to make this assumption of no payback, or the game is over in the first generation. On net, the aggregate change in consumption of apples is zero even though it is dramatically different between the two Cohorts.

The second generation inherits the debt problem. For sake of simplicity we assume the debt is inherited by the AP children and the bonds by the AW children. In this generation, if no additional deficit is run up then we end up with a situation where Cohort BW consumes 10 more apples than they would have otherwise from the continued interest on the bonds. Cohort AP consumes 10 less from the interest. Again, on net the change in consumption in aggregate from what would have happened if that debt did not exist is zero.

Let's assume we get to generation C. The Cohort CW now want the entirety of their apples back that are owed to them. Assuming Cohort AP has a legal obligation to pay this money as they would in real life, they pay back the full 100 apple principle. Cohort CP is now 100 apples poorer than they would have been, but Cohort CW is 100 apples richer. Again, in aggregate the change in consumption of apples from what would have happened if that debt didn't exist is zero. Even if we assume Cohort CP defaults and can't pay back its apples, Cohort AW is SOL and will not have the 100 more apples it wanted. On net we are back at a zero sum game.

However, if we assume the default scenario what you end up with is Cohort Ps having had the pleasure of consuming 80 more apples than it otherwise would have if the mediator (government) did not ring up a deficit and AW had 80 less.

My thinking is that you are only considering generational shift without distributional shift. It seems like the government is being treated as it's own foreign entity to which apples are owed and not just a middle man distributor.

Otherwise, without tax, there is perpetual rollover of debt, and the "we owe it to ourselves" argument is valid.

It's not valid if there is a future tax to pay down the debt.

And how you slice and dice the generational difference doesn't really matter in that context. Nick's model simplifies things to a net generational demarcation line between B and C. But the point is that C ends up paying, whoever they happen to be, or whatever their actual generational composition.

once you assume that, you can generalize the definition of what is meant by a "future generation" ex post facto, merely by defining the cohort that pays the taxes in that way - in fact, that defined cohort may well be a mixture of people, some of whom benefited from the original transfer, and some of whom didn't - Nick's model just splits them out cleanly into a purely future generation, by construction

And the question of whether or not the assumption of a future tax to pay down the debt is a reasonable assumption is an entirely separate issue - that's where you get into MMT type arguments that its silly to assume that; but that's a separate argument from the analysis of what the nature of the generational impact of an assumed future tax is

So, in one sense, it's distribution problem of Y within each period, as Krugman states. Nonetheless, intergeneration inequality ensues, as Nick emphasizes.
However, cohort C doesn't have to bear all the pain. If the pain is intertemporally diversified, the inequality would be eased. And that intertemporal diversification of burden is also what Krugman frequently make a point of.

This is all academia at it’s worst. It angles on pin heads all over again. The crucial question is: DO OLDIES ACTUALLY SELL BONDS TO YOUNGSTERS? My answer is that to all intents and purposes in the real world THEY DON’T (for reasons I gave above).

I can make silly assumptions. Here’s one: my car is made of gold. Conclusion: I’m fabulously wealthy – a conclusion which is pure hot air.

I understand what you are saying about the assumption of a future tax, and maybe I haven't thought through the concept of overlapping enough, but the proceeds of that future tax seem to go toward paying the owners of the bonds/IOUs which are still one half of the same whole. Ultimately, in this example the taxes go back to the descendants of the wealthy cohort to be consumed and the aggregate consumption of the generation of the cohorts that pay the tax and receive the tax is still net zero. If the first transfer during Cohort A is essentially writing up and handing an IOU to Cohort A, then the essential impact of paying the tax during Cohort C is simply burning the IOUs.

In the end the bonds still seem to be a tax liability to yourself, assuming you are the beneficiary of the government finances. By definition in this example we assume apples can't be stored and therefore all apples will be consumed in a generation. Assuming no productivity increases, cohort group B will end up paying 10% interest on an apple deal they didn't originate, but that doesn't matter because they are paying those apples back to the government middle man which is effectively a straight transfer back to themselves (assuming no loss in transfer).

Sorry if I am slow to catch on, I find this post extremely interesting.

JKH: "Krugman implicitly assumes no future taxes to pay down the debt."

A quibble. Yes. But he also explicitly talks about the increased taxes implied by the debt.

himaginary: "So, in one sense, it's distribution problem of Y within each period, as Krugman states. Nonetheless, intergeneration inequality ensues, as Nick emphasizes."

Yep. Good way of stating it.

Ralph: "The crucial question is: DO OLDIES ACTUALLY SELL BONDS TO YOUNGSTERS? My answer is that to all intents and purposes in the real world THEY DON’T (for reasons I gave above)."

Um, then who exactly do the oldies sell their bonds to? Do they take them to their graves like some sort of Viking funeral? Or do they *give* them to their kids (in which case we are assuming Ricardian Equivalence, so bond-financed tax cuts don't do anything)?

Cont...
It seems the assumption of selling bonds to Cohort B doesn't make much sense without considering the other side of the economic transaction. It looks like Nick is assuming that when Cohort A goes into the transaction with Cohort B, they sell the 110 apples worth of bonds and are free to eat a pot load of apples. The reality is that when Cohort A goes to sell the bonds to Cohort B, they are holding the asset of 110 bonds in one hand and a liability of 110 apples of payment in the other. They have to convince Cohort B that somehow having an asset of 110 future apples and a debt of 110 apples is somehow worth 110 apples of payment to Cohort A. Instead Nick is treating the government as a separate entity that houses the debt side of the transaction while the cohorts house the asset side. I don't see why we would not treat the government as the same entity as the people. If we do, the value of the IOUs and the debt of the IOUs cancel out and the idea of selling the bonds is nonsensical.

chase: assume you are a young Canadian and I am an old Canadian. Assume Canada is a closed economy for simplicity.

If I offered to sell you a Canadian government bond, (and the price were right), would you buy it? Yes. It's a good way for you to save for your old age.

Now, suppose all the old Canadians like me clubbed together. And all the young Canadians like you clubbed together. If my club offered to sell you our Canadian government bonds would your club buy them? Possibly not. Your club might reason that if it refused to buy our bonds, then us old Canadians would be unable to do anything with them except take them to our graves with us. So your club could wipe out the national debt, and be able to pay lower taxes.

What is individually rational for each young person isn't necessarily collectively rational for all young people.

Nick, Re your question “who do they sell their bonds to?”, my answer is that in the real world some oldies sell their bonds on the open market. The buyers will tend to be youngsters / middle aged people building up pension pots. Alternatively, oldies in their retirement run down their claims on pension schemes (which invests to some extent in bonds), while youngsters build up their claims on such schemes. But this amounts to the same thing as oldies selling bonds to youngsters.

If we are agreed on that I think we are also agreed that there at there are two things that oldies can do with their bonds. 1. Give them to their kids (or to some charity, or whoever). 2. Sell their bonds to youngsters / the middle aged.

Re “1.” I think we are agreed that no burden is passed on to the next generation. Re “2” I think we are agreed that this DOES pass on a burden. But my point is that there is little reason to suppose an INCREASED incidence of such selling or burden just because government debt rises.

Ergo an increase in government debt will not cause a significant increased burden on future generations.

Having said that, this whole issue is more complicated than I thought prior to Krugman’s article and your response to it. I used to be a member of the “time travel isn’t possible” brigade. And I now see that it’s a lot more complex than that.

Re Ricardianism, I think that’s a load of old hogwash (to use technical economics jargon). I set out my reasons here:

I definitely agree with you that what is rational at an individual level is not necessarily rational as a group and vice versa. So, does this all go out the window if we assume the currency is money instead of apples? If I am a young canadian and want one of those wonderful Canadian bonds for retirement, I will be buying it with cash. The old Canadian is not likely to go to his grave with those dollars or eat them, he is likely to go buy apples from a store that a young person works at or owns and the money ends up right back in the young generation. We now have an IOU and debt residing in the younger generation like we did under the apple scenario, but the money that left the generation came right back into the generation. Now, when they decided to tax to pay back the bond, the money is transferred from the owner of the apple store back to the bond owner in the same generation.

And Y is now down in apples, COMPARED to its starting position – i.e. it is “short” apples

But it does own bonds

Now compare that with the case where Y inherits the bonds from O

That means Y is not down apples, compared to its starting position – i.e. it is “flat” apples

Now consider the final leg of the entire sequence, which is the imposition of a tax on Y to pay down the debt

That constitutes a transaction in which Y effectively swaps maturing bonds that it owns in exchange for extinguishing a tax liability

That final transaction is the same whether Y bought or inherited the bonds from O – it matters only that Y owns the bonds, not how they got them, for this part of the sequence

So the end result is that the difference in the two final positions is due to the penultimate transaction where Y either buys or inherits the bonds – and Y is either short or flat apples as a result respectively relative to its starting position.

BTW, that second last paragraph I just wrote at 1:55, which describes the "self-liquidating" nature of the tax liability using the bonds that the tax is intended to pay down, has something to do with what I said elsewhere about Ricardian equivalence being a tautology at the macro level - the debt itself represents macro saving that is always available to pay the tax, which in turn is imposed to pay down the debt - this is a swap, and its circular, and its a tautology in that macro sense

If people have Rational Expectations, they won't buy Govt because they won't suffer from 'Bond illusion'. bonds.
Ricardian Equivalence is a red herring.
What's the point, 40 years on from the collapse of the Phillips curve, of a model in which agents are assumed to be stupid, irrational, and having a smaller information set than the Govt?

every person has 100 apples. take 10 off those younger than 10 and give them to those older than 90. (assume linear pop. dist.) the young eat 90 apples, the old eat 110 and promptly die (or you shoot them)

in this sense you are right that there is a burden on "future generations" meaning the young, but it is not at all like apples have travelled back in time.

assume there is 1 person at every age and everyone dies when they hit 100. in each year 10,000 apples grow on trees and are eaten. its just that you eat 90 ages 0-9 and 110 ages 91-100

i say NB

(also P and NP usually stand for polynomial and non-polynomial time class of problems, not generically Proposition and negation of proposition although people who don't have comp. sci. degrees might use them in this loose fashion???)

"if the generation that benefitted from the deficit is already dead, it's too late to make the choice to tax them. They have consumed the deficit, and you can't get them to pay higher taxes from the grave."

yes but theres no deficit. you simply cancel the deficit. re my example above in time T+1 where the old people have died after eating more apples, the new crop of 10,000 apples comes in, 10,000 apples demanded (100 per person) and consumed so you just cancel the transfer program whenever you want to and theres no burden on the future.

if you think of this in simple physical goods terms you realise there is No B

there is a one off (or many one offs =) transfer from young to old, but you can't have some mysterious created burden forever on the future, it violates physics, and economists aren't allowed to do that yet =)

nick's example above has been going on for a million years, god comes down a la tower of babel and destroys all memory of the scheme and all accounting debt and tax records...everything.

the then population of X cohorts all just eat the apples produced that year. what happened to that strange burden (answer it never existed)

the only way there can be a burden on future generations is the government taxes someone at some time and destroys apples (or leaves them to rot) but this is not the burden of debt, it is the burden of stupid government policy at any time T.